Spatially resolved measurements of absolute oxygen atom concentrations in low-pressure H2/O2/Ar-, CH4/O2- and C2H2/O2 flames are performed by two-photon laser excited fluorescence. The measured signals are converted into O atom number densities using a calibration technique, based on the comparison of fluorescence signals in a flame with those in a discharge flow reactor. This procedure requires consideration of quenching processes; furthermore, the influence of photoionization and potential photodissociation of flame gases must be considered. The sensitivity of the derived concentrations to experimental parameters and atomic quantities is discussed.